Skeletal supermanifolds \(\mathcal {M}\)  of dimension \(m|k\)  can be constructed starting from a rank \(k\)  real vector bundle \(E\)  over an \(m\) -dimensional ordinary manifold \(|\mathcal {M}|\) . We just set that the sheaf of functions on \(\mathcal {M}\)  is isomorphic to the set \(\Gamma (|\mathcal {M}|,\Lambda ^*E)\)  of smooth sections of the exterior algebras bundle \(\Lambda ^*E\)  over \(|\mathcal {M}|\) . We denote by \(S(|\mathcal {M}|,E) = \mathcal {M}\)  this supermanifold and call it a split supermanifold (see e.g. [1]}). A theorem by M. Batchelor [2]} asserts that any supermanifold has a split structure.
